# Optimal and robust noncausal filter formulations

@article{Einicke2006OptimalAR, title={Optimal and robust noncausal filter formulations}, author={Garry A. Einicke}, journal={IEEE Transactions on Signal Processing}, year={2006}, volume={54}, pages={1069-1077} }

The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother. The optimal solution involves a cascade of a Kalman predictor and an adjoint Kalman predictor. A robust smoother involving H/sub /spl infin// predictors is also described. Filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error. These bounds lead to a priori estimates for the scalar /spl gamma/ in the H/sub /spl infin…

## 33 Citations

Discrete-time Smoothing Formulas

- MathematicsTENCON 2005 - 2005 IEEE Region 10 Conference
- 2005

The paper presents the discrete-time minimum- variance fixed-interval smoother for linear output estimation problems and an extended Kalman smoother for nonlinear problems. The solutions involve a…

Robust extended Kalman filtering for nonlinear systems with multiplicative noises

- Engineering, Mathematics
- 2011

In this paper, we investigate the robust filter design problem for nonlinear systems with multiplicative noises. The aim of the problem is to design a state estimator with a predictor–corrector…

A Solution to the Continuous-Time H ∞ Fixed-Interval Smoother Problem

- Mathematics

—The minimum-variance fixed-interval smoother is a state-space realization of the Wiener solution generalized for time-varying problems. It involves forward and adjoint Wiener-Hopf factor inverses in…

Properties of a continuous-time H∞ fixed-interval smoother

- Mathematics2007 46th IEEE Conference on Decision and Control
- 2007

It is shown that the smoother exhibits an increase in mean-square-error, the error is bounded, and the upper error bound is greater than that for the Hinfin filter.

Iterative Smoother-Based Variance Estimation

- MathematicsIEEE Signal Processing Letters
- 2012

The minimum-variance smoother solution for input estimation is described and it is shown that the resulting estimates are unbiased. The smoothed input and state estimates are used to iteratively…

Optimum minimum variance fixed interval smoothing

- EngineeringProceedings of the Eighth International Symposium on Signal Processing and Its Applications, 2005.
- 2005

Speech enhancement and nonlinear demodulation examples are presented which demonstrate that optimal and extended Kalman smoothers can provide performance benefits.

A Particle Filter Approach to Robust State Estimation for a Class of Nonlinear Systems with Stochastic Parameter Uncertainty

- Engineering, MathematicsIEICE Trans. Fundam. Electron. Commun. Comput. Sci.
- 2011

A robust state estimation method using a particle filter (PF) for a class of nonlinear systems which have stochastic parameter uncertainties and can be applied regardless of system stability.

A Solution to the Continuous-Time ${\rm H}_{\infty}$ Fixed-Interval Smoother Problem

- MathematicsIEEE Transactions on Automatic Control
- 2009

It is shown that the smoother exhibits an increase in mean-square-error, the error is bounded, and the upper error bound is greater than that for the H∞ filter.

Asymptotic convergence of Riccati equation and smoother solutions

- Mathematics2007 46th IEEE Conference on Decision and Control
- 2007

It is shown that when the Riccati equation solutions converge, the time-varying, minimum-variance, fixed-interval smoothers provide optimal performance.

Variational Inference of Kalman Filter and Its Application in Wireless Sensor Networks

- Computer ScienceInt. J. Distributed Sens. Networks
- 2013

An improved Kalman filter algorithm by using variational inference (VIKF) is proposed and results show that the variational approximation is effective and reliable for the linear state space, especially for the case with time-varying non-Gaussian noise.

## References

SHOWING 1-10 OF 40 REFERENCES

H/sub infinity /-minimum error state estimation of linear stationary processes

- Mathematics
- 1990

A state estimator is derived which minimizes the H/sub infinity /-norm of the estimation error power spectrum matrix. Two approaches are presented. The first achieves the optimal estimator in the…

Robust steady-state filtering for systems with deterministic and stochastic uncertainties

- Computer Science, MathematicsIEEE Trans. Signal Process.
- 2003

This work presents filtering algorithms that solve each of these problems, with the filter parameters determined via convex optimization based on linear matrix inequalities, and demonstrates the performance of these robust algorithms on a numerical example consisting of the design of equalizers for a communication channel.

Robust extended Kalman filtering

- EngineeringIEEE Trans. Signal Process.
- 1999

A new approach to the robust design of a discrete-time EKF is presented by application of the robust linear design methods based on the H/sub /spl infin// norm minimization criterion to demonstrate an advantage for signal demodulation and nonlinear equalization applications.

On discrete-time H∞ fixed-lag smoothing

- Mathematics, Computer Science
- 2004

Efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H∞ filtering Riccati equation, which provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.

On discrete-time H/sub /spl infin// fixed-lag smoothing

- Mathematics, Computer ScienceIEEE Transactions on Signal Processing
- 2004

Efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H/sub /spl infin// filtering Riccati equation, which provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.

Filtering and smoothing in an H/sup infinity / setting

- Mathematics
- 1991

The problems of filtering and smoothing are considered for linear systems in an H/sup infinity / setting, i.e. the plant and measurement noises have bounded energies (are in L/sub 2/), but are…

The use of fake algebraic Riccati equations for co-channel demodulation

- EngineeringIEEE Trans. Signal Process.
- 2003

A method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system and is compared with an EKF for a co-channel frequency demodulation application.

The independance of forward and backward estimation errors in the two-filter form of the fixed interval Kalman smoother

- Mathematics
- 1980

In this paper it is shown that the Fraser-Potter two-filter form of the fixed interval Kalman smoother can be derived without assuming that the forward and backward estimation errors are independent.…

An innovation approach to H∞ fixed-lag smoothing for continuous time-varying systems

- MathematicsIEEE Trans. Autom. Control.
- 2004

A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H/sub /spl infin// fixed-lag smoother.